Subgroups — #14521441

Order 1984.

124 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#92482	C₂	1	2	yes	maximal, complemented
3	C₂×#92481	C₂	1	2	yes	maximal
4	#11758452	C₂	1	1	yes	maximal, characteristic
5	#11758391	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×Q₈×C₃₁	C₂²	1	2	yes	—
7	C₂×D₁₂₄	C₂²	1	1	yes	characteristic
8	C₂×Dic₆₂	C₂²	1	1	yes	characteristic
9	C₄⋊C₄×C₃₁	—	2	2	no	—
10	C₄²×C₃₁	C₂²	1	1	yes	characteristic
11	#92482	—	2	4	no	—
12	#92481	—	2	4	no	—
13	(C₂×D₃₁)⋊C₄	—	2	2	no	—
14	C₂×C₃₁⋊C₈	C₂²	1	2	yes	—
15	C₂²×D₃₁	—	2	1	no	—
16	Q₈×C₃₁	—	2	2	no	—
17	Q₈×C₃₁	—	2	2	no	—
18	C₂×C₄×C₃₁	—	2	2	no	—
19	C₂×C₄×C₃₁	D₄	1	2	yes	—
20	C₂×C₄×C₃₁	C₂³	1	1	yes	characteristic
21	C₂×Dic₃₁	—	2	1	no	—
22	D₁₂₄	—	2	2	no	—
23	Dic₆₂	—	2	2	no	—
24	C₃₁⋊C₈	D₄	1	4	yes	—
25	C₂²×C₃₁	C₂×D₄	1	1	yes	characteristic
26	C₂×D₃₁	—	4	1	no	—
27	C₂×D₃₁	—	4	2	no	—
28	C₄×C₃₁	—	2	2	no	—
29	C₄×C₃₁	—	4	2	no	—
30	C₄×C₃₁	C₂×D₄	1	2	yes	—
31	Dic₃₁	—	4	1	no	—
32	#497	—	31	1	no	maximal, Sylow
33	C₂×C₃₁	#127	1	1	yes	characteristic
34	C₂×C₃₁	#137	1	2	yes	—
35	D₃₁	—	8	1	no	—
36	C₂×Q₁₆	—	31	2	no	—
37	C₂×SD₁₆	—	31	2	no	—
38	C₄⋊Q₈	D₃₁	1	1	yes	characteristic, complemented
39	#124	—	31	1	no	—
40	#97	—	31	1	no	—
41	C₃₁	#497	1	1	yes	characteristic, complemented, Sylow
42	C₂×Q₈	—	31	1	no	—
43	C₂×Q₈	C₂×D₃₁	1	2	yes	—
44	C₂×D₄	—	31	1	no	—
45	Q₁₆	—	62	4	no	—
46	SD₁₆	—	62	4	no	—
47	C₂×C₈	—	31	2	no	—
48	C₄⋊C₄	—	2	2	no	—
49	C₂²⋊C₄	—	62	2	no	—
50	C₄²	C₂×D₃₁	1	1	yes	characteristic
51	C₂³	—	62	1	no	—
52	Q₈	—	2	2	no	—
53	Q₈	—	2	2	no	—
54	Q₈	—	62	2	no	—
55	D₄	—	62	2	no	—
56	C₂×C₄	—	2	2	no	—
57	C₂×C₄	—	62	1	no	—
58	C₂×C₄	C₂²⋊D₃₁	1	2	yes	—
59	C₂×C₄	C₂²×D₃₁	1	1	yes	characteristic
60	C₈	—	31	4	no	—
61	C₂²	—	124	1	no	—
62	C₂²	—	124	2	no	—
63	C₂²	C₂×C₂²⋊D₃₁	1	1	yes	characteristic
64	C₄	—	2	2	no	—
65	C₄	—	4	2	no	—
66	C₄	—	124	1	no	—
67	C₄	D₄×D₃₁	1	2	yes	—
68	C₂	—	248	1	no	—
69	C₂	#11758517	1	1	yes	characteristic
70	C₂	#11758519	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₃₁
commutator, cosocle	C₂×C₄×C₃₁	C₂³
Frattini	C₂×C₄	C₂²×D₃₁
Fitting	C₃₁×C₄⋊Q₈	C₂
socle	C₂²×C₃₁	C₂×D₄
prime radical	C₂×D₁₂₄	C₂²
hypercenter	C₄⋊Q₈	D₃₁
hypocenter	C₃₁	#497
LCS	G ▷ C₂×C₄×C₃₁ ▷ C₂×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄⋊Q₈

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₃₁×C₄⋊Q₈	C₂	semidirect
2. C₂×#92482	C₂	semidirect
5. #11758391	C₂	semidirect
38. C₄⋊Q₈	D₃₁	semidirect
41. C₃₁	#497	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃₁×C₄⋊Q₈	2
C₂×#92482	2
C₂×#92481	2
#11758452	2
#11758391	2
#497	31